### Re: How do nonexpandable materials work?

Date: Mon Jul 3 09:10:27 2006
Posted By: David Ellis, Researcher, NASA Glenn Research Center
Area of science: Engineering
ID: 1151637418.Eg
Message:

Generally speaking the materials are described as low coefficient of thermal expansion (CTE) materials rather than nonexpandable materials. I suspect that the nonexpandable designation is a marketing term.

### Thermal Expansion

First, a quick background on thermal expansion.

Temperature is a reflection of the vibrational amplitude and frequency of atoms in a material. As the temperature increases the atoms vibrate more. The more they move, the greater the separation between atoms. For most materials that are unconstrained, the increasing separation between atoms will cause a change in length that is positive. This is the cause of thermal expansion.

It is also possible to have a material show a negative thermal expansion. That means it contracts when heated. Will Bray of Texas A&M University at Kingsville has a presentation here that explains this well (Microsoft Powerpoint, Powerpoint Viewer or OpenOffice required). The rearrangement of the microscopic unit cells making up the material into a more compact structure causes the macroscopic decrease in size. This is what is driving what you are seeing in the oven top.

The increase in length with temperature is approximately linear. Normally there is a slight positive deviation in the length over large temperature changes. The linear approximation allows the calculation of the coefficient of thermal expansion (CTE). This is the slope of the line when you plot the thermal strain (change in length divided by original length) versus temperature. In most cases it is expressed as ppm/K (parts per million per Kelvin) or ppm/°F (parts per million per degree Fahrenheit). By multiplying the CTE by the absolute temperature change you can calculate the thermally induced strain. Multiplying the strain by the initial length of the part gives the change in length of the part.

Thermal expansion behavior can change radically when the materials undergo a phase change. For example, pure iron at low temperatures will expand linearly up to 910°C (1670°F). At that point the atoms will rearrange themselves from a body centered cubic (BCC) configuration (a cube with one atom in the middle and eight atoms at the corners) to a face centered cubic (FCC) configuration (one atom at the center of the six faces and one atom at each corner). This will result in a decrease in volume, and the thermal expansion will show a sudden decrease if you are plotting it versus temperature. A classic demonstration is to heat a piano wire using electricity and watch it first sag and then suddenly snap tight when the phase change occurs.

### Low Thermal Expansion Materials

There are quite a few materials that have very low thermal expansions or near zero CTEs. Most tend to contain ceramics because their atoms tend to be held more tightly than other material classes such as metals and polymers (plastics). Many are composite materials - materials that contain two distinct materials often with radically different characteristics that combine their properties for improved performance.

Quartz is one of the best known low CTE material. Its expansion is about 0.5 ppm/K. This low thermal expansion allows it to be heated and then quenched in ice water without shattering as typical silica glass would. Several other ceramics exhibit similar CTEs. Quartz is hard, cheap and fairly inert, so the oven top may have been made from it. The downside to quartz is it is an insulator, but radiative and inductive heating can overcome this limitation.

Invar is an iron-nickel alloy that exhibits low CTE (<1.3 ppm/K from 20-100°C) up to about 230°C (446°F). It has a multitude of uses in scientific instruments, electronics, CRT displays, etc. It is probably not what is in the oven top because of the upper use temperature limitation, but it does illustrate a common low CTE material.

Another possibility is a composite made from graphite fibers. The graphite fibers used in sports equipment and other applications will contract when heated in the plane of the sheets of CA atoms but expand in the direction perpendicular to the sheets. The dependence of properties on direction is called anisotropy. The oven top may have been a composite containing graphite fibers woven in such a way as to make the overall oven top not expand or expand imperceptibly. Copper, aluminum or some other metal could be put around the fibers to hold them together and provide a good cooking surface. Some carbon fibers are also very conductive, so they would help distribute heat evenly, a good benefit for an oven top.

Another possibility is silicon carbide reinforced aluminum. In these composites silicon carbide, the grit used in some sandpapers, is infiltrated with molten aluminum to make a part. It is a fairly low thermal expansion material (typically (6-8 ppm/K) with excellent thermal conductivity and good chemical resistance. Cost is also lower than many other metal matrix composites since it is being used in electronics packaging and other thermal management applications that have allowed economies of scale to come into play. There is some limitation on maximum use temperature since aluminum melts at low temperatures (<660.37°C/1221ªF), but aluminum is used for cookware and could potentially work for an oven top.

Various glasses can also be combined with small particles of another phase to make colorful materials with low CTEs. Doping or adding a small amount of an element can also lower their CTEs though not to zero. The glasses and the particulates are typically quite cheap and resistant to both temperature and common cooking ingredients. My guess lacking the specifics of which oven top and manufacturer to which you refer is that the oven top has some sort of doped glass with a few percent of a negative CTE material such as zirconium tungstate added to further reduce the thermal expansion.

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